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On association and other forms of positive dependence for Feller processes

Part of: Distribution theory - Probability Markov processes

Published online by Cambridge University Press:  30 July 2019

Eddie Tu
Eddie Tu*
Affiliation:
Dickinson College
*
*Postal address: Department of Mathematics and Computer Science, Dickinson College, PO Box 1773, Carlisle, PA 17013, USA.
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Abstract

We characterize various forms of positive dependence, such as association, positive supermodular association and dependence, and positive orthant dependence, for jump-Feller processes. Such jump processes can be studied through their state-space dependent Lévy measures. It is through these Lévy measures that we will provide our characterization. Finally, we present applications of these results to stochastically monotone Feller processes, including Lévy processes, the Ornstein–Uhlenbeck process, pseudo-Poisson processes, and subordinated Feller processes.

Keywords

Associationsupermodular dependencesupermodular associationorthant dependenceFeller processLévy processintegro-differential operatorsymbols

MSC classification

Primary: 60E07: Infinitely divisible distributions; stable distributions 60E15: Inequalities; stochastic orderings 60J25: Continuous-time Markov processes on general state spaces 60J35: Transition functions, generators and resolvents 60J75: Jump processes

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 56 , Issue 2 , June 2019 , pp. 624 - 646
Copyright
© Applied Probability Trust 2019 

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